Suppose a geometry keeps Euclid's first four postulates but assumes that through an external point there pass exactly TWO distinct lines parallel to a given line. How does the angle sum of a triangle compare with 180° in such a (hyperbolic-type) geometry?

Question

Accepted Answer

It is less than 180°. When more than one parallel is allowed (hyperbolic geometry), the angle sum of a triangle is LESS than 180°, unlike Euclidean geometry where it equals 180°.

Suppose a geometry keeps Euclid's first four postulates but assumes that through an external point there pass exactly TWO distinct lines parallel to a given line.
How does the angle sum of a triangle compare with 180° in such a (hyperbolic-type) geometry?

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More Class 9 The Fifth Postulate practice

Suppose a geometry keeps Euclid's first four postulates but assumes that through an external point there pass exactly TWO distinct lines parallel to a given line.How does the angle sum of a triangle compare with 180° in such a (hyperbolic-type) geometry?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 9 The Fifth Postulate practice

Suppose a geometry keeps Euclid's first four postulates but assumes that through an external point there pass exactly TWO distinct lines parallel to a given line.
How does the angle sum of a triangle compare with 180° in such a (hyperbolic-type) geometry?